{"paper":{"title":"Semi-Synchronous Exploration in Dynamic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Mobile agents cannot explore 1-interval connected dynamic graphs if an adversary deactivates ceil(k/(n-2)) - 1 or more agents per round.","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Anisur Rahaman Molla, Ashish Saxena, Gokarna Sharma, Kaushik Mondal","submitted_at":"2026-05-14T04:54:34Z","abstract_excerpt":"We study the fundamental problem of graph exploration in dynamic graphs using mobile agents. We consider $1$-interval connected dynamic graphs, where the topology may change arbitrarily from round to round as long as the graph remains connected, and edges are assigned with the dynamic port labeling at each round. The execution follows a semi-synchronous scheduler, under which an adversary may deactivate an arbitrary subset of agents in each round. For a graph with $n$ nodes and $k$ agents, we show that exploration is impossible if the adversary can deactivate at least $ \\left\\lceil \\frac{k}{n-"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that exploration is impossible if the adversary can deactivate at least ceil(k/(n-2)) - 1 agents per round, even when agents are equipped with unbounded memory, have global communication and full visibility. This yields an upper bound, implying that exploration is solvable only when the adversary deactivates at most ceil(k/(n-2)) - 2 agents per round.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The underlying graph remains 1-interval connected in every round (connected despite arbitrary edge changes) with dynamic port labeling; the semi-synchronous adversary model and the specific visibility/communication capabilities are also load-bearing.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exploration of 1-interval connected dynamic graphs with k agents is impossible if an adversary deactivates at least ceil(k/(n-2))-1 agents per round and is achievable if at most ceil(k/(n-2))-2 are deactivated, requiring 1-hop visibility and communication.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Mobile agents cannot explore 1-interval connected dynamic graphs if an adversary deactivates ceil(k/(n-2)) - 1 or more agents per round.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3b887cda412b4f3a745c71fa3e24ea5284d20ce26c6d7a2abd4eff7f99af8ab0"},"source":{"id":"2605.14375","kind":"arxiv","version":1},"verdict":{"id":"46b6813e-b4fa-4c77-ba92-f66e84d95b4f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:51:18.157806Z","strongest_claim":"We show that exploration is impossible if the adversary can deactivate at least ceil(k/(n-2)) - 1 agents per round, even when agents are equipped with unbounded memory, have global communication and full visibility. This yields an upper bound, implying that exploration is solvable only when the adversary deactivates at most ceil(k/(n-2)) - 2 agents per round.","one_line_summary":"Exploration of 1-interval connected dynamic graphs with k agents is impossible if an adversary deactivates at least ceil(k/(n-2))-1 agents per round and is achievable if at most ceil(k/(n-2))-2 are deactivated, requiring 1-hop visibility and communication.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The underlying graph remains 1-interval connected in every round (connected despite arbitrary edge changes) with dynamic port labeling; the semi-synchronous adversary model and the specific visibility/communication capabilities are also load-bearing.","pith_extraction_headline":"Mobile agents cannot explore 1-interval connected dynamic graphs if an adversary deactivates ceil(k/(n-2)) - 1 or more agents per round."},"references":{"count":19,"sample":[{"doi":"","year":1993,"title":"C. E. Shannon, Presentation of a maze-solving machine, Claude Elwood Shannon Collected Papers (1993) 681–687","work_id":"d663ef7e-5224-4e7d-9754-065776a5bf23","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Das, Graph exploration with mobile agents, in: Chapter 16 of Handbook of Graph Theory, Combinatorial Optimization, and Algorithms, 2019, pp","work_id":"7548fe63-5f63-4357-8848-2e60e37aba3b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"F. Kuhn, N. Lynch, R. Oshman, Distributed computation in dynamic networks, in: STOC’2010, Association for Computing Machinery, New York, NY, USA, p. 513–522","work_id":"f0635edd-758d-47fc-b79b-7e70d40de9d0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"A. Casteigts, P. Flocchini, W. Quattrociocchi, N. Santoro, Time-varying graphs and dynamic networks, International Journal of Parallel, Emergent and Distributed Sys- tems 27 (5) (2012) 387–408","work_id":"bed8a761-1305-400d-b265-fb31eb5f6e65","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"O. Michail, I. Chatzigiannakis, P. G. Spirakis, Causality, influence, and computa- tion in possibly disconnected synchronous dynamic networks, Journal of Parallel and Distributed Computing 74 (1) (201","work_id":"40dfc17b-b7e3-400f-80fc-83504e82f4ad","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":19,"snapshot_sha256":"5a71ce067af6388c25d715e44c010ab48d912d7241bc5382fb8ef8764e25c78e","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}